Dynamical Imaging Using Spatial Nonlinearity
Speaker: Christopher Barsi
Series: Final Public Orals
Location: Engineering Quadrangle J401
Date/Time: Monday, October 24, 2011, 10:30 a.m. - 12:30 p.m.
The limitations of linear imaging were succinctly formalized by Ernst Abbe in 1873. In his theory, an object is treated as an ensemble of Fourier modes, each of which acts individually as a diffraction grating. Spatial modes can be detected only if the wavenumbers of the lowest diffraction orders lie within the spatial bandwidth, limited by the numerical aperture, of the system Otherwise, they—and the corresponding features—are lost.
Nonlinear optics can break these limits by exploiting the presence and interaction of many photons at once. Previous work explored this option using the mixing of only temporal frequencies, whereas the interaction of spatial modes has been neglected or suppressed. As spatial modes are the ones that comprise an image (rather than represent its color), they are significant.
In this work, Abbe’s theory of diffraction is generalized to include wave interactions. The underlying dynamical propagation of spatial modes will be explored and introduced into computational imaging techniques. Then, using spatial nonlinearity as a new degree of freedom, experimental demonstration of nonlinear imaging beyond the diffraction limit is presented.